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Question 1 (10 Marks)
Let A, B and C be three sets as follows:
A = {1, 2, 3, 4, 5, 6, 7}
B = {3, 5, 7, 9, 11}
C = {4, 6}
Determine each of the following:
i.  (7, B)
ii.  (B, A)
iii. ∪ (A, C)
iv. ∩ (B, C)
v. \ (B, A)
Question 2 (13 Marks)
Prove that n2 ≥ n2
- 2n + 15 ∀ n ≥ 8
by mathematical induction.
Question 3 (12 Marks)
Postage ticket of amount  n0 cents can be formed using only 5 cent and 9 cent coins. You are
required to find the minimum n0.
Question 4 (15 Marks)
Start with some special kind of pair of rabbits, one male and one female, born on January 1.
Assume all months are of equal length and no rabbit dies. After reaching the age of three months,
each pair produces one mixed pair (one male and one female), and then two mixed pairs every
two months thereafter. Give a recursive mathematical model to compute the number of pairs of
rabbits for a given month.

Question no 4

Recursive Mathematical Model;
Total pairs at level k = Total pairs at level k-1 + Total pairs born at level k .....(1)
Since
Total pairs born at level k = ? ( Total pairs at level k-?)….(2)
Hence from equation (1) and (2) , we get the total pair at level k
Total pairs at level k = Total pairs at level k-1 + ? ( Total pairs at level k-?)
Let, Fk = Total pairs at level k
Then recursive mathematical model will be
Fk = Fk-1 +  Fk-?

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